Compatibility of whole-stand and individual-tree models using composite estimators and disaggregation

This study presents a new approach in linking models with different levels of resolution. Data from 50 permanent sample plots installed in even-aged birch (Betula alba) dominated stands were used to develop both, a whole-stand growth model and an individual-tree model. In a first step, six disaggregation approaches to link number of trees per hectare with tree survival were combined with four disaggregation approaches to link stand basal area with tree basal area growth predictions. To analyze the effect of stand variable predictions on disaggregation estimates, two different methods to obtain these predictions were evaluated: (a) 1-fold cross-validation of the stand growth model and (b) a method involving composite estimators. Therefore, altogether 48 different approaches in linking models were analyzed in this first step. In a second step, two common methods based on the use of a threshold to translate the survival tree probabilities into a discrete event, i.e. dead or alive, were combined with the four disaggregation approaches to link stand basal area with tree basal area growth predictions and the two methods to obtain stand variable predictions. Therefore, altogether 16 different approaches in linking models were analyzed in this second step. Finally, the best combinations obtained in each step were compared. Regarding the disaggregation of predicted stand density, the approach based on considering the intercept of the logit function for tree survival as a specific parameter of each sample plot and optimizing its value produced the best results. Regarding the disaggregation of stand basal area among trees, the constrained least squares method was selected, since it showed the best results among four alternative approaches. The use of composite estimators instead of the 1-fold cross validation predictions improved the accuracy of both, tree survival and tree basal area estimates, although the differences were not significant. Finally, disaggregation approaches performed better than the methods based on the use of a threshold. The results show that the combination between composite estimators and disaggregation provided compatible and reliable predictions of stand density, tree survival, stand basal area and tree basal area. The main limitation of this new approach is the dependency of accurate stand growth predictions, therefore, it should be tested in future studies with more complicated stand structures, such as mixed and un-even aged forests, or to include the effect of silvicultural treatments.